Kiara bakes 40 oatmeal cookies and 48 chocolate chip cookies in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container had the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need? How many oatmeal cookies and how many chocolate chip cookies will be in each container?
GCD(40,48) = 8
So there will be 8 batches of cookies.
Can you finish it from here?
Yep! Thank you!!!!
To find the number of plastic containers Kiara needs, let's first determine the greatest common divisor (GCD) of 40 and 48. The GCD is the largest number that divides both 40 and 48 evenly.
To find the GCD, you can use the Euclidean algorithm:
Step 1: Divide 48 by 40. The result is 1 with a remainder of 8.
Step 2: Divide 40 by 8. The result is 5 with no remainder.
Step 3: The last nonzero remainder is 8. Therefore, the GCD of 40 and 48 is 8.
Since the GCD of 40 and 48 is 8, each plastic container will have 8 cookies: 8 oatmeal cookies and 8 chocolate chip cookies.
Now, let's calculate the number of plastic containers Kiara needs. There are a total of 40 oatmeal cookies and 48 chocolate chip cookies. Since each container will have 8 cookies, we divide the total number of cookies by 8:
Total number of cookies = 40 (oatmeal) + 48 (chocolate chip) = 88
Number of plastic containers needed = 88 ÷ 8 = 11
Therefore, Kiara will need 11 plastic containers. Each container will have 8 cookies: 8 oatmeal cookies and 8 chocolate chip cookies.